Observer-oriented dynamic hybrid-triggered control for semi-Markovian jump PDE systems with generally uncertain transition rates

The objective of this research is to examine issue of the quantized dynamic hybrid-triggered disturbance rejection control for parabolic PDE systems under a semi-Markovian jump process amid generally uncertain transition rates and multiple disturbances. Specifically, the matched disturbances caused by exogenous systems can be effectively handled through the implementation of a mode-dependent output disturbance observer that estimates with high accuracy. Simultaneously, the (A1,A2,A3)−p dissipative performance minimises the adverse effects of mismatched disturbances. Thereafter, a mode-dependent proportional-integral estimator has been proposed, which incorporates both proportional and integral components to estimate the states of the system under analysis. Additionally, the dynamic hybrid-triggered technique are implemented, which results in reduction of superfluous communication within the network. Thereafter, the observer-based quantized dynamic hybrid-triggered disturbance rejection controller is designed to ensure stabilisation and disturbance rejection of the appraised systems. Following this, the mode-dependent Lyapunov-Krasovskii functional along with some integral inequalities is utilised to derive the requisite criteria in terms of linear matrix inequalities. Lastly, two numerical examples along with graphical illustrations are provided to showcase the capabilities and effects of the developed controller approach.